eng
Science and Education Publishing
American Journal of Numerical Analysis
2328-7292
2014-10-12
2
5
144
151
10.12691/ajna-2-5-2
AJNA2014252
article
Optimal Quadrature Formulas with Polynomial Weight in Sobolev Space
Kholmat M. Shadimetov
1
Abdullo R. Hayotov
hayotov@mail.ru
1
Sardor I. Ismoilov
1
Institute of Mathematics, National University of Uzbekistan, Do‘rmon yo‘li str., Tashkent, Uzbekistan
In this paper we construct the optimal quadrature formula with polynomial weight in the Sobolev space L2(m)(0,1). Using S.L. Sobolev's method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula.
http://pubs.sciepub.com/ajna/2/5/2/ajna-2-5-2.pdf
optimal quadrature formulas
error functional
extremal function
sobolev space
optimal coefficients